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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Partitions into chains of a class of partially ordered sets


Authors: N. Metropolis, Gian-Carlo Rota, Volker Strehl and Neil White
Journal: Proc. Amer. Math. Soc. 71 (1978), 193-196
MSC: Primary 06A10; Secondary 05B99
MathSciNet review: 0551483
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Abstract: Let a cube of side k in $ {{\mathbf{R}}^n}$ be dissected into $ {k^n}$ unit cubes. The collection of all affine subspaces of $ {{\mathbf{R}}^n}$ determined by the faces of the unit cubes forms a lattice $ L(n,k)$ when ordered by inclusion. We explicitly construct a Dilworth partition into chains of $ L(n,k)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0551483-6
PII: S 0002-9939(1978)0551483-6
Article copyright: © Copyright 1978 American Mathematical Society



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